The number of mosquitoes is increasing at an estimated rate r(t)=2200+e^0.8(t) per week (where t is measured in weeks). By how much does the mosquito population increase between the fifth and ninth week?

Question

whpalmer4 · Answer

Ah, but it says that r(t) is a rate of increase, not a population...

Also, very unclear (at least to me) exactly what the period over which the increase happens is.  Does "between the fifth and ninth week" include the 5th week?  How about the 9th week?

whpalmer4 · Answer

We don't need it, do we?  The rate doesn't depend on the population (at least not explicitly).

whpalmer4 · Answer

That should probably be
$$\int_5^9 \left(e^{0.8 s}+2200\right) \, ds$$

whpalmer4 · Answer

No, not what I get....I get 10,406, which seems about right.

anonymous · Answer

@whpalmer4 , you are right and I am wrong.

anonymous · Answer

10,406 is the  answer

whpalmer4 · Answer

If I compute r(t) for each of t=5,6,7,8 the results are 2254, 2321, 2470, 2802
that will underestimate the population change slightly

whpalmer4 · Answer

I just hope you're right about that being the right answer :-)

anonymous · Answer

....

anonymous · Answer

@hartnn Mister_kid_dynamite above me is spamming multiple questions with the same answer "...." and in each of them he has a medal for best response. Something fishy is going on.

hartnn · Answer

Thanks for pointing it out! I'll look into this :)